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  • Sum of series:
  • a^n
  • (-1)^n*(2*2)^(2*n)/factorial(2*n) (-1)^n*(2*2)^(2*n)/factorial(2*n)
  • log(n+1)/(n+1) log(n+1)/(n+1)
  • 38 38

  • Identical expressions

  • two ^2x*(x- one / four)x
  • 2 squared x multiply by (x minus 1 divide by 4)x
  • two squared x multiply by (x minus one divide by four)x
  • 22x*(x-1/4)x
  • 22x*x-1/4x
  • 2²x*(x-1/4)x
  • 2 to the power of 2x*(x-1/4)x
  • 2^2x(x-1/4)x
  • 22x(x-1/4)x
  • 22xx-1/4x
  • 2^2xx-1/4x
  • 2^2x*(x-1 divide by 4)x

  • Similar expressions

  • 2^2x*(x+1/4)x
Sum of series/ 2^2x*(x-1/4)x

Sum of series 2^2x*(x-1/4)x


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The solution

You have entered [src] 
  oo                 
 __                  
 \ `                 
  )   4*x*(x - 1/4)*x
 /_,                 
n = 1
$$\sum_{n=1}^{\infty} x 4 x \left(x - \frac{1}{4}\right)$$ 
Sum(((4*x)*(x - 1/4))*x, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$x 4 x \left(x - \frac{1}{4}\right)$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = 4 x^{2} \left(x - \frac{1}{4}\right)$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
    2           
oo*x *(-1/4 + x)
$$\infty x^{2} \left(x - \frac{1}{4}\right)$$ 
oo*x^2*(-1/4 + x)

    Examples of finding the sum of a series

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